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anonymous

  • 4 years ago

If a , b, and c are in Arithmetic Progression, then the straight line ax + by + c = 0 will always pass through the point: a) (- 1, -2) b) (1, -2) c) (-1 , 2) d) (1, 2)

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  1. anonymous
    • 4 years ago
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    Please help.

  2. amistre64
    • 4 years ago
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    we should know that the slope of the line is: -a/b

  3. amistre64
    • 4 years ago
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    0 = -a/b x - c is then what we have to conform to i believe

  4. anonymous
    • 4 years ago
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    I think so.

  5. amistre64
    • 4 years ago
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    well, -c/b on the end i spose would be more accurate

  6. amistre64
    • 4 years ago
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    when x=0, -c/b = 0 means that c=0 so: y = -a/b x seems like a fair assumption

  7. amistre64
    • 4 years ago
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    i gotta re think that :)

  8. amistre64
    • 4 years ago
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    ax +by + c = 0 ax + by = -c y = (-ax -c) /b no zero involved .....

  9. asnaseer
    • 4 years ago
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    If a, b and c are in AP, then doesn't this imply: b = a + d c = a + 2d where d is the difference between each term of the AP?

  10. amistre64
    • 4 years ago
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    good, good

  11. anonymous
    • 4 years ago
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    Then, how to proceed next?

  12. amistre64
    • 4 years ago
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    if my line equation is useful; maybe sub in so that it all speaks in a?

  13. asnaseer
    • 4 years ago
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    Then you can rewrite your equation as: ax + (a+d)y + a + 2d = 0 and see for which point this equation holds true?

  14. amistre64
    • 4 years ago
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    \[y = \frac{-ax -(a+2d)}{a+d}\] would be the same set up i believe

  15. asnaseer
    • 4 years ago
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    yes it would

  16. anonymous
    • 4 years ago
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    So the exact option?

  17. asnaseer
    • 4 years ago
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    Aadarsh: just put each pair of values into the equations and see which one works

  18. amistre64
    • 4 years ago
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    a) (- 1, -2) b) (1, -2) c) (-1 , 2) d) (1, 2) trial and error .... \[-2 \ =^? \frac{a -(a+2d)}{a+d}\] \[-2 \ =^? \frac{-a -(a+2d)}{a+d}\] \[2 \ =^? \frac{a -(a+2d)}{a+d}\] \[2 \ =^? \frac{-a -(a+2d)}{a+d}\]

  19. amistre64
    • 4 years ago
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    \[2 \ =^? \frac{-a -(a+2d)}{a+d}\] \[2 \ =^? \frac{-a -a-2d}{a+d}\] \[2 \ =^? \frac{-2a-2d}{a+d}\] \[2 \ =^? -2\frac{a+d}{a+d};F\]

  20. amistre64
    • 4 years ago
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    -1,-2 would then seem to be appropriate to me

  21. anonymous
    • 4 years ago
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    Is it? I wrote (-1, -2), just guessing.

  22. asnaseer
    • 4 years ago
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    amistre: I get a different result. Aadarsh: what do you get?

  23. amistre64
    • 4 years ago
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    i got a typo in my cerbral cortex; :) 1,-2 might be better; would have to test it out

  24. asnaseer
    • 4 years ago
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    :) - I concur

  25. anonymous
    • 4 years ago
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    Yes, (1, -2) is the only correct answer.

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